The heterotic string theory can embeds the crossed gauge group SU(5) x
SU(5). Here we investigate the string unification in this framework
and the concerning problems. We show generically that only a very
constrained parameter space is allowed for new particles, mostly due
to the gauge coupling constant \alpha_1^{-1}. One possible but
unfavourable solution is given by the introduction of three fermion
generations of SU(5)_L-adjoint representation. Only the low-scale
decompositions of SU(5)_L with vanishing hypercharge ((1,3)_0 triplets
and (8,1)_0 octets) of both fermionic and bosonic types can be
included to circumvent the problem. The triplets must live in TeV
region and could be accessible at colliders. We also show that
non-supersymmetric scenario is exclusively compatible with the
introduction of additional color-SU(2)_L-triplet field while
supersymmetry is only possible at high-energy scale. All these
intermediated thresholds are easily incorporated into the called
Adjoint SU(5) schemes